An elementary bound for the number of points of a hypersurface over a finite field (Summary)

This short note is a summary of our paper with the same title [M. Homma and S. J. Kim, An elementary bound for the number of points of a hypersurface over a finite field, preprint 2012]. We establish an upper bound for the number of points of a hypersurface without a linear component over a finite field, which is analogous to the Sziklai bound for a plane curve.